Let D be the set of all calendar dates from 4/30/1789 to 9/25/2014., homework help

May 3rd, 2016
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Question description

Let D be the set of all calendar dates from 4/30/1789 to 9/25/2014.
Let P be the set of names of U.S. presidents.
Let F be the set of names of first ladies of the U.S.

Consider the following two functions pres:D \rightarrow P where pres(d) is the name of the president of the U.S. on date d (the incumbent on inauguration days, to avoid ambiguity) and lady:P \rightarrow F where lady(p) is the name of the first lady of the U.S. during the presidency of president p.

1. Can the composition pres \circ lady be defined? What about lady \circ pres?

2. Which of the following functional inverses exist and which do not?
 pres^{-1}lady^{-1}(lady \circ pres)^{-1}
 (pres \circ lady)^{-1}

Tutor Answer

(Top Tutor) Daniel C.
School: UC Berkeley

Answer 1. No, the composition  cannot be defined because co-domain of the function is not same as the domain of the...

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May 3rd, 2016
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